Revisiting the pure annihilation decays $B_s\to \pi^+ \pi^-$ and $B^0 \to K^+ K^-$: the data and the pQCD predictions

TL;DR

This paper recalculates pure annihilation B meson decays using pQCD, compares predictions with experimental data, and finds good agreement and potential for CP asymmetry detection.

Contribution

It provides a consistent pQCD interpretation for measured decay rates and offers new predictions for CP asymmetry in B meson decays.

Findings

pQCD predictions align with experimental measurements

Predicted CP asymmetry is approximately 16%

Different authors' predictions for $Br(B_s^0 o \pi^+\pi^-)$ are consistent

Abstract

In this work, we recalculate the charmless pure annihilation decays $B_s\to \pi^+ \pi^-$ and $B^0 \to K^+ K^-$ by using the perturbative QCD (pQCD) factorization approach, and compare the pQCD predictions with currently available experimental measurements. We used the same set of relevant input parameters and wave functions to make the calculations for the considered decay modes and found the following results: (a) one can provide a consistent pQCD interpretation for both the measured $Br(B_s^0 \to \pi^+ \pi^-)$ and $Br(B_d^0 \to K^+ K^-)$ simultaneously; (b) the pQCD predictions for $Br(B_s^0 \to \pi^+\pi^-)$ obtained by different authors are well consistent with each other; (c) our new pQCD prediction for $Br(B_d^0 \to K^+K^-)$ agree very well with the measured values from CDF and LHCb Collaboration; and (d) the CP-violating asymmetry ${\cal A}_{CP}(B_d^0 \to K^+K^-) \approx 16%$, which is large and may be detected at the LHCb experiment.